Which one is which?

@Orbit Newflavor, the one on the left is the closed timeline curve computer from the Xeelee sci fi series, it's a temporal devices that work using FTL data that travel back in time and answer questions before they're asked. It breaks down problems into pieces and recursively solve them with time travel without the temporal paradox allowing for acausality. It brute force their way through every potential calculation, then send the correct answer back in time once it's been found, it do not wear out because they send the answer back before they even need to run on energy supply.

The right is path to victory which is pretty self explanatory.

I chose the one I am the least bit knowledgeable with

Path to Victory. I'm not sure I understand the Processor. Is it an artifact? Is it verse-specific, that is, can you only scan the future of the verse you are in? One of the problems I want to solve is escaping our own gravity-well verse, so PTV is, perhaps, a safer bet.

@Two-of-Six, well it's similar to path to victory that it gets give you the answers to a outcome but before questions even take place that how fast it is, CTCs Device work under the presupposition that "basic Xeelee verse time travel is acasual", which means killing a person in the past doesn't delete him from the present, he just continues to exist in the present, causality doesn't exist, due to configuration space and all that. CTC processors work on this principle, there is no temporal paradox, the information appears out of nothing from a future that never was. To sum it up it like mixing coil timeline splitting power, contessa PTV and phir se time transport in one device that can be linked inside a brain or a machine.

So the processor is a literal computer processor that essentially achieves computational supertasking via acausal time travel?

@AzQth, yes it's a computer that brute-force calculates information before sending said information back in time in a series of time-loops.